Could this be Between Heaven and Earth (1992)? The IMDb description says
A week before its delivery, a baby warns his pregnant mother he doesn't want to come out in this world and prefers to die instead.
The date fits, as does the plot about babies refusing to be born. The main character, Maria, is a journalist who is expecting when she meets another woman at her obstetrician's office who claims her fetus is talking to her. Maria herself starts having dreams where her baby is talking to her, saying it doesn't want to be born into our world.
Other fetuses are staying in the womb, they tell their mothers in dreams, because they don't want to be born. They don't like what the world has become and they don't want to live like us.
Boston Globe Review, archived
She goes to the hospital to be induced, but hears someone saying how many stillbirths have been happening, so she leaves and instead tries to convince her child to be born.
There's a bit more detail in a review on the New York Times site and some additional links (though not much more information) on the Wikipedia page.